A simple explanation for the decrease in interest rates with an increase in money supply is that the price of all products reaches an equilibrium which is dependent on the supply and the demand of the product.

The rate of interest can considered to be the price of money. As with any other product, a relative increase in supply of the product for the same demand leads to a decrease in the price.

Lenders like banks or other financial institution, first need to acquire the funds that they are able to lend. With an increased money supply this is easier to do and is also less expensive. Therefore they can lend at a lower rate of interest and still make a profit. Any lender who charges a high rate of interest would lose customers who are attracted to other competing lenders with better offers in terms of lower rates of interest.